Aircraft Design
AET 3513
Sizing from a Conceptual
Sketch
Dr Raed Kafafy
Dr Raed Kafafy
Aircraft Design (AET 3513)
Introduction
❑ Sizing is the first and most important calculation in aircraft conceptual design.
❑ Sizing finds how big and heavy the airplane must be to attain the required mission:
flying the required range and carrying the design payload.
❑ The drawing is based on the sizing results, which are used to find the dimensions of
the engine, wings, tires, fuel tanks, tails, etc.
❑ Sizing literally determines the size of the aircraft, specifically the weight that the
aircraft must be designed to so that it can perform its intended mission carrying its
intended payload.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Introduction
❑ Each aircraft mission is described by a set of mission requirements from which
design requirements are derived.
❑ Design requirements must be rigorously analyzed and then used to develop a number
of candidate designs (design concepts), each of which must be designed, analyzed,
sized, optimized, and redesigned any number of times.
❑ The best candidate sized to its minimum weight to perform the required mission will
be the selected design candidate to proceed with.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Design Wheel.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Aircraft conceptual design process.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Sizing Methods
❑ There are many levels of aircraft sizing procedure.
❑ The simplest level just adopts past history.
▪ For example, if you need an immediate estimate of the takeoff weight of an airplane to replace
the Air Force F-15 fighter, use 44,500 lb. That is the design weight of the F-15 and is probably a
fair number to start with, if you are in a hurry.
❑ Sophisticated sizing procedures involve analysis techniques which include all manner
of computer code as well as correlations to wind-tunnel and other tests (even with this
extreme level of design sophistication, the actual airplane when flown will never
exactly match predictions).
❑ In between these extremes of sizing procedure lie the methods used for most
conceptual design activities.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Our Sizing Method
❑ The sizing method presented here is a quick sizing method, which will allow you to
estimate required takeoff weight from
1. conceptual sketch and
2. sizing mission.
❑ The method introduces all of the essential features of the most sophisticated sizing
methods used by the major aerospace manufacturers.
❑ The method is most accurate when used for missions that do not include any combat or
payload drops.
❑ Later, the concepts introduced here will be expanded to a sizing method capable of
handling all types of missions and with greater accuracy.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Takeoff-Weight Buildup
❑ Design takeoff gross weight is the total weight of the aircraft as it begins the mission
for which it was designed.
❑ It is not necessarily the same as the maximum takeoff weight (MTOW) (many
military aircraft can be overloaded beyond the design weight but will suffer reduced
maneuverability).
❑ Unless otherwise mentioned, takeoff gross weight is assumed to be the design
weight.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Takeoff-Weight Buildup
❑ Design takeoff gross weight (𝑊0 ) can be broken into:
▪ crew weight (𝑊𝑐𝑟𝑒𝑤 ),
▪ payload (or passenger) weight (𝑊𝑝𝑎𝑦𝑙𝑜𝑎𝑑 ),
▪ fuel weight (𝑊𝑓𝑢𝑒𝑙 ), and
▪ the remaining (or empty) weight (𝑊𝑒𝑚𝑝𝑡𝑦 ).
❑ The takeoff weight buildup equation can be written as
𝑾𝟎 = 𝑾𝒄𝒓𝒆𝒘 + 𝑾𝒑𝒂𝒚𝒍𝒐𝒂𝒅 + 𝑾𝒇𝒖𝒆𝒍 + 𝑾𝒆𝒎𝒑𝒕𝒚
▪ This equation is also referred to as weight distribution.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Takeoff-Weight Buildup
❑ Empty weight includes: the structure, engines, landing gear, fixed equipment,
avionics, and anything else not considered a part of crew, payload, or fuel.
❑ 𝑊𝑐𝑟𝑒𝑤 and 𝑊𝑝𝑎𝑦𝑙𝑜𝑎𝑑 are both known (they are given in the design requirements).
❑ The only unknowns are the 𝑊𝑓𝑢𝑒𝑙 and 𝑊𝑒𝑚𝑝𝑡𝑦 (both are dependent on the total
aircraft weight; so we should use an iterative process).
❑ To simplify the calculation, 𝑊𝑓𝑢𝑒𝑙 (= 𝑊𝑓 ) and 𝑊𝑒𝑚𝑝𝑡𝑦 (= 𝑊𝑒 ) are expressed as fractions
of total takeoff weight – that is (𝑊𝑓 /𝑊0 ) and (𝑊𝑒 /𝑊0).
❑ Thus, we can rewrite the weight distribution equation as
𝑊𝑓
𝑊𝑒
𝑊0 = 𝑊𝑐𝑟𝑒𝑤 + 𝑊𝑝𝑎𝑦𝑙𝑜𝑎𝑑 +
𝑊0 +
𝑊0
𝑊0
𝑊0
Dr Raed Kafafy
Aircraft Design (AET 3513)
Takeoff-Weight Buildup
❑ If we solve for 𝑊0 , then we get
𝑾𝒄𝒓𝒆𝒘 + 𝑾𝒑𝒂𝒚𝒍𝒐𝒂𝒅
𝑾𝟎 =
𝑾𝒇
𝑾𝒆
𝟏− 𝑾 − 𝑾
𝟎
𝟎
❑ 𝑊0 can be determined if 𝑊𝑓 Τ𝑊0 and 𝑊𝑒 Τ𝑊0 can be estimated.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Empty-Weight Estimation
❑ After the aircraft has been drawn, the actual empty weight will be calculated by
estimating and summing the weights of all of the components of the aircraft.
❑ For now it can be estimated as a fraction 𝑊𝑒 Τ𝑊0 using simpler methods.
❑ The empty-weight fraction 𝑊𝑒 Τ𝑊0 can be estimated statistically from historical
trends.
Dr Raed Kafafy
Aircraft Design (AET 3513)
• The right figure (developed by Raymer from data
taken from several sources) presents empty
weight fraction as function of sized takeoff
weight for different types of aircraft.
• Empty-weight fractions which vary from about
0.3 to 0.7 diminish with increasing total aircraft
weight.
• It can be seen that the type of aircraft also has
a strong effect (flying boats have the highest
empty-weight fractions and long-range military
aircraft have the lowest.)
• Notice also that different types of aircraft exhibit
different slopes to the trend lines of emptyweight fraction vs takeoff weight.
Empty-weight fraction trends.
Dr Raed Kafafy
Aircraft Design (AET 3513)
𝑾𝒆 Τ𝑾𝟎 = 𝑨𝑾𝑪𝟎 𝑲𝒗𝒔
• The right table presents statistical curve-fit
equations for the trends in the previous
figure.
• Note that these are all exponential
equations based upon takeoff gross weight
(pounds or kilograms).
• The exponents are small negative numbers,
which indicates that the empty-weight
fractions decrease with increasing takeoff
weight, as shown by the trend lines.
• The differences in exponents for different
types of aircraft reflect the different slopes
of their trend lines and imply that some
types of aircraft are more sensitive in sizing
than others.
The variable sweep constant 𝐾𝑣𝑠 is equal to 1.0 unless the
aircraft has variable-sweep wing (such as F-111).
Dr Raed Kafafy
Aircraft Design (AET 3513)
Empty Weight Fraction vs 𝑊0
Empty-Weight Estimation
❑ While the presented figure and table can be used for initial estimation of 𝑊𝑒 Τ𝑊0 , it's
always better to develop your own trendline.
❑ Composite materials such as graphite-epoxy are replacing aluminum in many new
designs; however there still no enough composite aircraft to develop good statistical
equations for them.
❑ So, we will approximate 𝑊𝑒 Τ𝑊0 for a composite aircraft by multiplying the
estimated statistical empty-weight fraction by 0.95. Later we'll analyze the weights in
some detail, and learn if this was about right.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Fuel-Fraction Estimation
❑ We also need to estimate the fuel available to perform the mission.
❑ Simple statistical methods will not work - we need to fly the aircraft over its required
mission.
❑ Only part of aircraft fuel supply is available for performing the mission (mission fuel).
❑ The other fuel includes reserve fuel as required by civil or military design
specifications (mostly to allow for degradation of engine performance) and also
includes trapped fuel (fuel that cannot be pumped out of the tanks).
𝑊𝑓 = 𝑊𝑚𝑖𝑠𝑠𝑖𝑜𝑛 𝑓𝑢𝑒𝑙 + 𝑊𝑟𝑒𝑠𝑒𝑟𝑣𝑒 𝑓𝑢𝑒𝑙 + 𝑊𝑡𝑟𝑎𝑝𝑝𝑒𝑑 𝑓𝑢𝑒𝑙
Dr Raed Kafafy
Aircraft Design (AET 3513)
Fuel-Fraction Estimation
❑ The required amount of mission fuel depends upon
▪ aircraft mission to be flown
▪ aerodynamics of the aircraft
▪ engine fuel consumption
▪ aircraft weight (aircraft weight during the mission affects the drag, so that the fuel used is a
function of the aircraft weight).
❑ As a first approximation, the fuel used can be considered to be proportional to the
aircraft weight, so that the fuel fraction (𝑊𝑓 Τ𝑊0 ) is approximately independent of
aircraft weight.
❑ Fuel fraction can be estimated based on the mission to be flown using approximations
of the fuel consumption and aerodynamics.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Mission Profiles
❑ Here we consider typical mission profiles.
❑ The Simple Cruise mission is used for many transport and general-aviation designs,
including homebuilt aircraft.
▪ The aircraft is sized to provide some required cruise range.
▪ For safety you would be wise to carry extra fuel in case your intended airport is closed, so a
loiter of typically 20-30 min [at 10,000 ft or 3,048 m] is added.
▪ Alternatively, additional range could be included, representing the distance to the nearest other
airport or some fixed number of minutes of flight at cruise speed.
Under commercial IFR regulations, you also need fuel to fly to an alternate airport after loitering and attempting
to land at your intended destination.
The FAA requires 30 min of additional cruise fuel for daytime flights under visual flight rules (VFR), and 45 min
of fuel at night or under instrument conditions (IFR).
Dr Raed Kafafy
Aircraft Design (AET 3513)
Mission Profiles
❑ The low-level strike mission includes "dash" segments that must be flown at just a few
hundred feet off the ground.
▪ This is to improve the survivability of the aircraft as it approaches its target.
▪ Unfortunately, the aerodynamic efficiency of an aircraft, expressed as lift-to-drag ratio (𝐿/𝐷), is
greatly reduced during low-level, high-speed flight, as is the engine efficiency.
▪ The aircraft may burn almost as much fuel during the low-level dash segment as it burns in the
much-longer cruise segment.
❑ The typical air superiority mission includes a cruise out, a combat consisting of either a
certain number of turns or a certain number of minutes at maximum power, a weapons
drop, a cruise back, and a loiter.
▪ The weapons drop refers to the firing of gun and missiles and is often left out of the sizing analysis to
ensure that the aircraft has enough fuel to return safely if the weapons are not used.
▪ Note that the second cruise segment is identical to the first, indicating that the aircraft must return to
its base at the end of the mission.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Typical mission profiles for sizing.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Mission-Segment Weight Fractions
❑ For analysis, the various mission segments, or legs, are numbered sequentially.
❑ For simple cruise mission we have
0 start of the mission.
1 warm-up and takeoff
2 climb
3 cruise
4 loiter
5 land
❑ During each mission segment, the aircraft loses weight by burning fuel. (Remember
that our simple sizing method doesn't permit missions involving a payload drop.)
Dr Raed Kafafy
Aircraft Design (AET 3513)
Mission-Segment Weight Fractions
❑ In a similar fashion, the aircraft weight at each part of the mission can be numbered.
𝑊0 = beginning weight (takeoff gross weight)
𝑊1 = weight at the end of the first mission-segment, which is the warm-up and takeoff.
𝑊2 = aircraft weight at the end of the climb.
𝑊3 = weight after cruise.
𝑊4 = weight after loiter.
𝑊5 = weight at the end of the landing segment, which is also the end of the total mission.
❑ For our simplified form of initial sizing, the types of mission leg will be limited to
warm-up and takeoff, climb, cruise, loiter, and land.
❑ Mission legs involving combat, payload drop, and refuel are not permitted in this
simplified sizing method.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Mission-Segment Weight Fractions
❑ The aircraft weight at the end of a mission segment divided by its weight at the
beginning of that segment is called the "mission segment weight fraction."
❑ This will be the basis for estimating the required fuel fraction for initial sizing.
❑ For any mission segment 𝑖, the mission segment weight fraction can be expressed as
(𝑊𝑖 /𝑊𝑖−1 ).
❑ If these weight fractions can be estimated for all of the mission legs, they can be
multiplied together to find the ratio of the aircraft weight at the end of the total
mission, 𝑊𝑥 (assuming 𝑥 segments altogether) divided by the initial weight 𝑊0 .
❑ The ratio 𝑊𝑥 /𝑊0 can then be used to calculate the total fuel fraction required.
❑ Mission-segment weight fractions can be estimated by a variety of methods.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Mission-Segment Weight Fractions
❑ Mission-segment weight fractions can be estimated by a variety of methods.
❑ The warm-up, takeoff, and landing weight fractions can be estimated historically.
❑ The table below gives typical historical values for initial sizing.
❑ These values can vary somewhat depending on aircraft type, but the averaged values
given in the table are reasonable for initial sizing.
Historical Mission-Segment Weight Fractions
Dr Raed Kafafy
Aircraft Design (AET 3513)
Mission-Segment Weight Fractions
❑ Cruise-segment mission weight fractions can be found using the Breguet range
equation
𝑅=−
𝑉𝐿
𝑊𝑖
ln
𝐶𝐷
𝑊𝑖−1
❑ Or
𝑊𝑖
−𝑅𝐶
= exp
𝑊𝑖−1
𝑉 𝐿Τ𝐷
❑ where
▪ 𝑅 = range (ft or m)
▪ 𝐶 = specific fuel consumption
▪ 𝑉 = velocity (ft/s or m/s)
▪ 𝐿Τ𝐷 = lift-to-drag ratio
Dr Raed Kafafy
Aircraft Design (AET 3513)
• 𝐶 and 𝐿/𝐷 vary with speed and altitude.
• Furthermore, 𝐶 varies with throttle setting, and 𝐿/𝐷 varies
with aircraft weight.
• These variations will be ignored at this level of analysis.
Mission-Segment Weight Fractions
❑ Loiter weight fractions are found from the endurance equation
1𝐿
𝑊𝑖
𝐸=−
ln
𝐶𝐷
𝑊𝑖−1
❑ Or
𝑊𝑖
−𝐸𝐶
= exp
𝑊𝑖−1
𝐿/𝐷
❑ where
▪ 𝐸 = endurance or loiter time (s)
Note It is very important to use consistent units!
Dr Raed Kafafy
Aircraft Design (AET 3513)
Specific Fuel Consumption – Jet
❑ Specific fuel consumption (SFC or simply 𝐶) is the rate of fuel consumption divided
by the resulting thrust.
❑ For jet engines, specific fuel consumption is measured in fuel mass flow rate per unit
thrust force.
▪ In British units, SFC is in pounds of fuel per hour per pound of thrust, that is lb/hr/lb (or 1/hr).
▪ In metric units we use mg/N-s.
❑ Note that for a jet aircraft, the SFC is function of flight velocity and altitude.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Specific Fuel Consumption – Propeller
❑ The engine produces thrust via the propeller, which has an efficiency 𝜂𝑝 defined as
thrust power produced by the propeller (thrust times velocity) divided by the engine
power provided to the propeller.
𝑇𝑉
𝑇𝑉
𝜂𝑝 =
=
𝑃
550 ℎ𝑝
❑ The 550 factor converts horsepower to power in consistent British units assuming that
𝑉 is in ft/s.
❑ A propeller thrust SFC equivalent to the jet-engine SFC can be calculated from
𝑉
𝐶 = 𝐶𝑏ℎ𝑝
550 𝜂𝑝
Note that: 1 bhp = 550 ft-lb/s.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Specific Fuel Consumption – Propeller
❑ Note that for a propeller aircraft, the thrust and the SFC are functions of flight velocity
and altitude.
❑ For a typical aircraft with a propeller efficiency of about 0.8, 1 hp equals one pound of
thrust at about 440 ft/s, or about 260 kt {484 km/h}.
❑ Typically, we can assume 𝜼𝒑 = 0.8 except for a fixed-pitch propeller during loiter,
where 𝜼𝒑 = 0.7 (These values are reasonable for rough initial sizing).
Dr Raed Kafafy
Aircraft Design (AET 3513)
• The right figure shows trend lines of SFC
versus Mach number for different types
of engines at typical cruise altitudes.
• Both British and metric units are shown
in the figure.
• For propeller engines (piston-prop and
turbo-prop), equivalent thrust SFC is
used.
Specific fuel consumption trends (at typical cruise altitudes).
Dr Raed Kafafy
Aircraft Design (AET 3513)
Specific Fuel Consumption
❑ The following tables provide typical SFC (= 𝐶) values for jet engines and typical 𝐶𝑏ℎ𝑝
values for propeller engines, respectively.
❑ Note that unit conversions will be required when you insert these values into the
cruise and loiter weight fraction equations to make sure that the units in the equations
are consistent.
❑ More detailed procedures for calculating specific fuel consumption as function of
altitude, velocity, and even power setting are used in more detailed sizing procedures.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Specific Fuel Consumption, 𝐶
Propeller Specific Fuel Consumption, 𝐶𝑏ℎ𝑝
Dr Raed Kafafy
Aircraft Design (AET 3513)
L/D Estimation
❑ The remaining unknown in both range and loiter equations is the 𝐿/𝐷 (lift-to-drag
ratio) which is a measure of the overall aerodynamic efficiency of the aircraft design.
❑ Unlike the previous parameters, the 𝐿/𝐷 is highly dependent upon the aircraft
configuration.
❑ At subsonic speeds 𝐿/𝐷 is most directly affected by two aspects of the design:
▪ wing span and
▪ wetted area (which is the total surface area of the aircraft exposed to the air).
Dr Raed Kafafy
Aircraft Design (AET 3513)
L/D Estimation
❑ In level flight, the lift is known (Lift = weight); thus, 𝐿/𝐷 is solely dependent upon
drag.
❑ The drag at subsonic speeds is composed of two parts:
▪ Induced drag (which is the drag caused by the generation of lift, which is primarily a function
of the wing span defined by wing aspect ratio).
▪ Parasite drag , or zero-lift drag (which is the drag that is not related to lift, which is primarily
skin-friction drag, and as such is directly proportional to the wetted area of the aircraft).
Wetted area of aircraft (𝑺𝒘𝒆𝒕 or 𝑺𝒘𝒆𝒕𝒕𝒆𝒅 ) is the total area of the entire aircraft surface which is in
contact (wetted by) the fluid (air).
Dr Raed Kafafy
Aircraft Design (AET 3513)
Wing geometry.
Dr Raed Kafafy
Aircraft Design (AET 3513)
L/D Estimation
❑ The aspect ratio of the wing has historically been used as the primary indicator of
wing efficiency.
❑ Aspect ratios range from under 1 for reentry lifting bodies to over 30 for sailplanes
with typical values ranging between 3 and 8.
❑ For initial design purposes, aspect ratio can be selected from historical data but for
final determination of the best aspect ratio, a trade study should be conducted.
❑ Estimation of subsonic lift-to-drag ratio requires both wing aspect ratio and aircraft
wetted area.
❑ Care should be given to the aircraft total wetted area, not just the wing area as
expressed by aspect ratio, because the parasite drag strongly depends on wetted area.
Dr Raed Kafafy
Aircraft Design (AET 3513)
L/D Estimation
❑ Two airplanes with similar span and total
wetted area will have a similar lift-to-drag
ratio, even if they look completely different
and their aspect ratios are dissimilar.
❑ In the right figure,
▪ The conventional wing design has an aspect ratio
of 7.7 typical for Boeing and Airbus airliners,
and attains a typical 𝐿/𝐷 max of 15.
▪ The delta wing design has an aspect ratio of only
3, yet it attains nearly the same 𝐿/𝐷 max - even
better.
Dr Raed Kafafy
Aircraft Design (AET 3513)
L/D Estimation
❑ The wetted-area ratio can be used, along with
aspect ratio, for an early estimate of 𝐿/𝐷.
❑ The right figure shows a spectrum of design
approaches and the resulting wetted-area ratios.
❑ 𝐿/𝐷 depends primarily on the wing span and the
wetted area, which suggests a new parameter, the
wetted aspect ratio 𝐴𝑤𝑒𝑡𝑡𝑒𝑑 defined as
𝑏2
𝐴
𝐴𝑤𝑒𝑡𝑡𝑒𝑑 =
=
𝑆𝑤𝑒𝑡 𝑆𝑤𝑒𝑡 /𝑆𝑟𝑒𝑓
where
𝐴 = 𝑏 2 /𝑆𝑟𝑒𝑓
Wetted area ratios.
Dr Raed Kafafy
Aircraft Design (AET 3513)
▪
The right figure plots 𝐿/𝐷 max for a number of aircraft vs
𝐴𝑤𝑒𝑡𝑡𝑒𝑑
▪
It shows clear trend lines for jet, prop, and fixed-gear prop
aircraft.
▪
These historical data are very useful for early prediction of
𝐿/𝐷, and for double-checking the results obtained from
detailed aerodynamic calculations.
▪
The trend lines could be extended far to the right for highaspect-ratio designs.
▪
The Global Hawk has a wetted aspect ratio of 6.8 and attains
an 𝐿/𝐷 max of over 35.
▪
High-performance sailplanes have wetted aspect ratios as high
as 12 and see a 𝐿/𝐷 max of 50 or more
Maximum lift-to-drag ratio trends.
Dr Raed Kafafy
Aircraft Design (AET 3513)
L/D Estimation
❑ An equivalent technique going back to the 1940s plots 𝐿/𝐷 vessus the square root of
wetted aspect ratio or
𝐴Τ 𝑆𝑤𝑒𝑡 Τ𝑆𝑟𝑒𝑓 .
❑ This format suggests the following equation for predicting 𝐿/𝐷 max
𝐿
𝐴
= 𝐾𝐿𝐷 𝐴𝑤𝑒𝑡𝑡𝑒𝑑 = 𝐾𝐿𝐷
𝐷 max
𝑆𝑤𝑒𝑡 Τ𝑆𝑟𝑒𝑓
where 𝐾𝐿𝐷 =
Dr Raed Kafafy
Aircraft Design (AET 3513)
15.5 for civil jets
14 for military jets
11 for retractable prop aircraft
9 for nonretractable prop aircraft
13 for high-aspect-ratio aircraft
15 for sailplanes
L/D Estimation
❑ Drag varies with altitude and velocity.
❑ For any altitude there is a velocity that maximizes 𝐿Τ𝐷.
❑ To maximize cruise or loiter efficiency, the aircraft should fly at approximately the
velocity for maximum 𝐿Τ𝐷.
❑ For initial sizing, the following table can be used to modify the values of 𝐿/𝐷 max
obtained from our previous prediction.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Mission-Segment Weight Fractions
❑ By multiplying weight fractions for all mission segments together, the total mission weight
fraction can be calculated.
❑ For a simple cruise mission, the total mission weight fraction is expressed as
𝑊5 𝑊1 𝑊2 𝑊3 𝑊4 𝑊5
=
×
×
×
×
𝑊0 𝑊0 𝑊1 𝑊2 𝑊3 𝑊4
❑ Typically 6% allowance is made for reserve and trapped fuel, so we can write
𝑊𝑓
𝑊5
= 1.06 1 −
𝑊0
𝑊0
Dr Raed Kafafy
Aircraft Design (AET 3513)
𝑊1
= warmup and takeoff weight fraction
𝑊0
𝑊2
= climb weight fraction
𝑊1
𝑊3
= cruise weight fraction
𝑊2
𝑊4
= loiter weight fraction
𝑊3
𝑊5
= landing weight fraction
𝑊4
Takeoff-Weight Calculation
❑ Using the estimated fuel fraction and the statistical empty weight fraction, the takeoff
gross weight can be found iteratively using the following algorithm:
1. Guess takeoff gross weight.
2. Calculate statistical empty-weight fraction.
3. Use estimated fuel weight fraction and empty-weight fraction to calculate takeoff gross weight.
4. If the result doesn't match our initial guess, take a value between the guessed value and the
calculated value as the new guess.
5. Go to step 2 and repeat until convergence.
𝑊𝑐𝑟𝑒𝑤 + 𝑊𝑝𝑎𝑦𝑙𝑜𝑎𝑑
𝑊0 =
❑ This algorithm will usually converge in few iterations.
Dr Raed Kafafy
Aircraft Design (AET 3513)
𝑊𝑓
1 − 𝑊 − 𝐴 𝑊0 𝐶
0
First-order design method.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Design Example: ASW Aircraft
❑ As a design and sizing example, consider the mission
requirement for a hypothetical antisubmarine warfare
(ASW) aircraft.
▪ The key requirement is the ability to loiter for 3 hr at a
distance of 1500 n miles {2778 km} from the takeoff point.
▪ While loitering on-station, this type of aircraft uses
sophisticated electronic equipment to detect and track
submarines.
▪ For the sizing example, this equipment is assumed to
weigh 10,000 lb {4536 kg}.
▪ Also, a four-man crew is required, totaling 800 lb {363 kg}.
▪ The aircraft must cruise at 0.6 Mach number.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Example mission profile.
Design Example: Conceptual Sketches
❑ Four conceptual approaches are considered by
the designer in response to the AWS mission
requirements.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Design Example: Conceptual Sketches
❑ Concept 1 is the conventional approach, looking
much like the Lockheed S-3A that currently
performs a similar mission. The low horizontal
tail position shown in solid line would offer the
lightest structure, but may place the tail in the
exhaust stream of the engines, so other positions
for the horizontal tail are shown in dotted lines.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Lockheed S-3A
Design Example: Conceptual Sketches
❑ Concept 2 is much like concept 1 except for the
engine location. Here the engines are mounted
over the wing. This provides extra lift due to
the exhaust over the wings and also provides
greater ground clearance for the engines, which
reduces the tendency of the jet engines to suck
up debris. The disadvantage of this concept is
the difficulty in reaching the engines for
maintenance work. Also, wing top engines
often suffer from interference drag.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Design Example: Conceptual Sketches
❑ Concepts 3 and 4 explore the canarded approach.
Canards offer the potential for reduced trim drag
and may provide a wider allowable range for the
center of gravity. However, it is often difficult to
put large flaps on the wing, so the wing must be
oversized.
❑ In concept 3, the wing is low and the engines are
mounted over the wing as in concept 2. This would
allow the main landing gear to be stowed in the
wing root, probably saving some weight and drag.
❑ In concept 4, the wing is high with the engines
mounted below. This last approach offers better
access to the engines.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Design Example: Conceptual Sketches
❑ Concepts 3 and 4 explore the canarded approach.
Canards offer the potential for reduced trim drag
and may provide a wider allowable range for the
center of gravity. However, it is often difficult to
put large flaps on the wing, so the wing must be
oversized.
❑ In concept 3, the wing is low and the engines are
mounted over the wing as in concept 2. This would
allow the main landing gear to be stowed in the
wing root, probably saving some weight and drag.
❑ In concept 4, the wing is high with the engines
mounted below. This last approach offers better
access to the engines.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Design Example: Conceptual Sketches
❑ The designer would be wise to take all four of
these concepts, and maybe a few more, on to
the next step of initial sizing and subsequent
design layout. In this example, only the last
approach (concept 4) will be illustrated.
❑ A conceptual sketch is prepared, in more
detail, for the selected concept.
Completed ASW sketch.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Design Example: Conceptual Sketches
▪ Note the locations indicated for the landing-gear stowage,
crew station, and fuel tanks.
▪ This points out a common problem with canard aircraft, the
fuel tank locations.
▪ The fuel tanks should be placed so that the fuel is evenly
distributed about the aircraft center of gravity (estimated
location shown by the circle with two quarters shaded).
▪ This is necessary so that the aircraft when loaded has nearly
the same center of gravity as when its fuel is almost gone.
▪ However, the wing is located aft of the center of gravity
whenever a canard is used, so that the fuel located in the
wing is also aft of the center of gravity.
Completed ASW sketch.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Design Example: Conceptual Sketches
▪ One solution to this problem would be to add fuel tanks in the
fuselage, forward of the center of gravity. This would increase
the risk of fire in the fuselage during an accident and is
forbidden in commercial aircraft. Although this example is a
military aircraft, fire safety should always be considered.
▪ Another solution, shown on the sketch, is to add a wing strake
full of fuel. This solution is seen on the Beech Starship among
others. The strakes do add to the aircraft wetted area, which
reduces cruise aerodynamic efficiency. This example serves to
illustrate an important principle of aircraft design.
▪ All aircraft design entails a series of tradeoffs. The canard
offers lower trim drag, but may require a larger wing and a
greater wetted area. The only way to determine whether a
canard is a good idea for this or any aircraft is to design
several aircraft, one with and one without a canard. This type
of trade study comprises the majority of the design effort
during the conceptual design process.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Completed ASW sketch.
Design Example: L/D Estimation
▪ For initial sizing of concept 4, a wing aspect ratio of
10 was selected.
▪ With the area of the wing and canard both included,
this is equivalent to a combined aspect ratio of
about 7.
▪ Comparing the conceptual design sketch to the
wetted area ratio figure, it would appear that the
wetted area ratio (𝑆𝑤𝑒𝑡 /𝑆𝑟𝑒𝑓 ) is about 5.5.
▪ This yields a wetted aspect ratio of 7/5.5 = 1.27.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Design Example: L/D Estimation
▪ For a wetted aspect ratio of 1.27, the maximum 𝐿/𝐷
figure indicates that a maximum lift-to-drag ratio of
about 16 would be expected.
▪ This value, obtained from an initial sketch and the
selected aspect ratio, can now be used for initial sizing.
▪ Because this is a jet aircraft, the maximum 𝐿/𝐷 is used
for loiter calculations.
▪ For cruise, a value of 0.866 × (𝐿Τ𝐷)max = 13.9 is used.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Design Example: Takeoff-Weight Sizing
❑ Initial values for SFC are obtained.
▪ For a subsonic aircraft the best SFC values are obtained with high-bypass turbofans, which
have typical values of about 0.5 for cruise and 0.4 for loiter.
❑ There is no specific statistical model for estimating the empty weight fraction of an
antisubmarine aircraft.
▪ However, such an aircraft is basically designed for subsonic cruise efficiency so that the
equation for military cargo/bomber can be used.
▪ The extensive ASW avionics would not be included in that equation, so it is treated as a
separate payload weight.
❑ The ASW sizing calculations are detailed in the next slide.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Note the unit conversions from
nmi to ft and from hr to s
1 nmi = 6076.12 ft
1 hr = 3600 s
Cruise velocity was calculated
from cruise Mach number = 0.6
by assuming typical cruise
altitude of 30 kft. At this altitude
the speed of sound is 994.8 ft/s.
Gross takeoff weight iterations
Dr Raed Kafafy
Aircraft Design (AET 3513)
Table 3.1
Table 3.2
Dr Raed Kafafy
Aircraft Design (AET 3513)
Design Example: Takeoff-Weight Sizing
❑ The calculations indicate a takeoff gross weight of
56,702 lb which is comparable to the actual takeoff
gross weight of the Lockheed S-3A quoted as
52,539 lb.
❑ The right figure illustrates an alternative way to
size the aircraft, by a graphical method.
❑ An Excel spreadsheet of this sizing example
illustrating both methods is available at
www.aircraftdesign.com/ac-size.html
Graphical sizing method for ASW example.
❑ The MATLAB function fzero can be used to solve
for the gross takeoff weight 𝑊0 as follows
fzero(@(W0) 10800/(1-0.3773-0.93*W0^(-0.07))-W0,50000)
Dr Raed Kafafy
Aircraft Design (AET 3513)
Trade Studies – Range Trade
❑ An important part of conceptual design is the evaluation and refinement of the design
requirements with the customer.
❑ In the ASW design example, the required range of 1,500 n miles (each way) is
probably less than the customer would really like.
❑ A range trade can be calculated to determine the increase in design takeoff gross
weight if the required range is increased.
❑ This is done by recalculating the weight fractions for the cruise mission segments,
using arbitrarily selected ranges.
❑ For example, instead of the required 1,500 n miles, we will calculate the cruise weight
fractions using 1,000 and 2,000 n miles and will size the aircraft separately for each of
those ranges.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Range Trade Calculations
Range trade
Dr Raed Kafafy
Aircraft Design (AET 3513)
Trade Studies – Payload Trade
❑ In a similar fashion, a "payload trade" can be made.
❑ The mission-segment weight fractions and fuel fraction are unchanged, but the
numerator of the sizing equation is parametrically varied by assuming different
payload weights.
❑ The given payload requirement is 10,000 lb of avionics equipment is varied by
assuming payload weights of 5,000 and 15,000 lb.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Payload Trade Calculations
Payload trade
Dr Raed Kafafy
Aircraft Design (AET 3513)
Trade Studies – Material Trade
❑ The statistical empty-weight equation used here for sizing was based upon existing
military cargo and bomber aircraft, which are all of aluminum construction.
❑ The preceding takeoff gross weight calculations have thus implicitly assumed that the
new aircraft would also be built of aluminum.
❑ To determine the effect of building the aircraft out of composite materials, the
designer must adjust the empty-weight equation.
❑ As mentioned earlier, this can be approximated in the early stages of design by taking
95% of the empty-weight fraction obtained for a metal aircraft.
❑ The use of composite materials reduces the takeoff gross weight from 56,702 lb {25,720
kg} to only 51,585 lb {23,399 kg}, yet the aircraft can still perform the same mission;
this is 9% takeoff-weight savings, results from only 5% empty-weight saving.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Trade Studies – Material Trade
❑ This result sounds erroneous, but is actually typical of the "leverage" effect of the
sizing equation.
❑ Unfortunately, this works both ways: If the empty weight creeps up during the detaildesign process, it will require a more-than-proportional increase in takeoff gross
weight to maintain the capability to perform the sizing mission.
❑ It is crucial that realistic estimates of empty weight be used during early conceptual
design, and that the weight be strictly controlled during later stages of design.
❑ There are many trade studies that could be conducted other than range, payload, and
material – methods for trade studies will be discussed in detail later.
Dr Raed Kafafy
Aircraft Design (AET 3513)
Composite Material Trade Calculations
Dr Raed Kafafy
Aircraft Design (AET 3513)